# 269edo

← 268edo | 269edo | 270edo → |

**269 equal divisions of the octave** (abbreviated **269edo** or **269ed2**), also called **269-tone equal temperament** (**269tet**) or **269 equal temperament** (**269et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 269 equal parts of about 4.46 ¢ each. Each step represents a frequency ratio of 2^{1/269}, or the 269th root of 2.

269edo is inconsistent in the 5-odd-limit and the errors of both harmonics 3 and 5 are quite large. The patent val tempers out 6144/6125 in the 7-limit, 540/539 and 5632/5625 in the 11-limit and 364/363 and 676/675 in the 13-limit. The 269c val tempers out 225/224 and 4375/4374 in the 7-limit, and 269ce 385/384 in the 11-limit, so that it supports and provides an excellent tuning for catakleismic and marvel temperaments.

### Odd harmonics

Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | Absolute (¢) | -1.58 | +1.79 | -0.80 | +1.29 | +1.84 | -1.87 | +0.21 | +2.11 | +1.37 | +2.08 | +0.72 |

Relative (%) | -35.5 | +40.1 | -17.8 | +29.0 | +41.3 | -41.8 | +4.6 | +47.2 | +30.7 | +46.7 | +16.2 | |

Steps (reduced) |
426 (157) |
625 (87) |
755 (217) |
853 (46) |
931 (124) |
995 (188) |
1051 (244) |
1100 (24) |
1143 (67) |
1182 (106) |
1217 (141) |

### Subsets and supersets

269edo is the 57th prime edo.